Related papers: Multiscale Analysis of Information Dynamics for Li…

Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…

Vector autoregressive (VAR) models are widely used in practical studies, e.g., forecasting, modelling policy transmission mechanism, and measuring connection of economic agents. To better capture the dynamics, this paper introduces a new…

We present a re-parameterization of vector autoregressive moving average (VARMA) models that allows estimation of parameters under the constraints of causality and invertibility. The parameter constraints associated with a causal invertible…

This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…

Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

In this paper physical multi-scale processes governed by their own principles for evolution or equilibrium on each scale are coupled by matching the stored and dissipated energy, in line with the Hill-Mandel principle. In our view the…

Vector AutoRegressive Moving Average (VARMA) models form a powerful and general model class for analyzing dynamics among multiple time series. While VARMA models encompass the Vector AutoRegressive (VAR) models, their popularity in…

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality,…

The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…

Complex adaptive systems (CAS) can be described as systems of information flows dynamically interacting across scales in order to adapt and survive. CAS often consist of many components that work towards a shared goal, and interact across…

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…

Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…

Consciousness spans macroscopic experience and microscopic neuronal activity, yet linking these scales remains challenging. Prevailing theories, such as Integrated Information Theory, focus on a single scale, overlooking how causal power…

Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is…

Computer-based interactive items have become prevalent in recent educational assessments. In such items, the entire human-computer interactive process is recorded in a log file and is known as the response process. This paper aims at…

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…